Problem: Solve for $x$ and $y$ using elimination. ${-x-6y = -27}$ ${-x+5y = 17}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $-1$ ${x+6y = 27}$ $-x+5y = 17$ Add the top and bottom equations together. $11y = 44$ $\dfrac{11y}{{11}} = \dfrac{44}{{11}}$ ${y = 4}$ Now that you know ${y = 4}$ , plug it back into $\thinspace {-x-6y = -27}\thinspace$ to find $x$ ${-x - 6}{(4)}{= -27}$ $-x-24 = -27$ $-x-24{+24} = -27{+24}$ $-x = -3$ $\dfrac{-x}{{-1}} = \dfrac{-3}{{-1}}$ ${x = 3}$ You can also plug ${y = 4}$ into $\thinspace {-x+5y = 17}\thinspace$ and get the same answer for $x$ : ${-x + 5}{(4)}{= 17}$ ${x = 3}$